Some modest Yahtzee goals

Probability Level 3

If the probability of getting at least one pair of matching dice when rolling five 6-sided dice is ab\frac{a}{b}, where aa and bb are positive co-prime integers, then what is a+ba+b?

Note: Three-of-a-kind, four-of-a-kind, full house, yahtzee, or two pairs would all count as "at least one pair of matching dice." However, a straight ({1,2,3,4,5}\{1,2,3,4,5\} or {2,3,4,5,6}\{2,3,4,5,6\}) or a small straight would not count.


Check out The anti-Yahtzee first to make finding the solution to this problem trivial.

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